Bridged t phase shifter



1952 P. H. RICHARDSON 2,585,342

BRIDGED T PHASE SHIFTER Original Filed Sept. 22, 1949 3 Sheets-Sheet 1 INVENTOR I? H. RICHARDSON L Mmmmz ATTORNEY 1952 P. H. RICHARDSON 2,535,842

BRIDGED T PHASE SHIFTER Original Filed Sept. 22, 1949 5 Sheets-Sheet 2 w' F/GQ FIG/0 A IN l EN TOR PH RICHARDSON WfW A TTORNEY Feb. 12, 1952 P. H. RICHARDSON 2,535,842

BRIDGED T PHASE SHIFTER Original Filed Sept. 22, 1949 3 Sheets-Sheet 5 FIG /5 4 FIG. /6 A //v l/EN 70/? I? h. RICHARDSON WVM ATTORNEY Patented Feb. 12, 1952 BRIDGED" 'r PHASEISHIFFTER" Paul H. Richardson, Chatham; N: J-i, assignor to Bell TelephoneLaboratories, Incorporated, New York, N. Y., a corporation ofiNewa York Original application September 2 2, 1949; Serial" No. 117,255. Divided and this application September 29,- 1950, Serial No:'187',493-- 23 Claims.- 1

This. invention relates to wave transmission networks and more particularly to variable phase shifters.

An object of the invention is to vary. the phase shift of awave transmission network over a wide range-without changing its image impedance.

Another object is to maintain a constant insertionloss at all settings of such a phase shifter.

Other objects are to simplifyv the circuit and reduce the size and cost of phase shifters of this type.

This is a division of my copending application Serial No. 117,255, filed September 22, 1949.

There is often required a. wave transmission network in which the phase shift at a single frequency may .be varied without changing the insertion loss or the image impedance.

image: impedance constant, both variable induc torsand variable capacitors are required.

The variable phase shifter of the present invention has the advantage that only. a single type of variable reactor, either a capacitor or an inductor, is required. In the unbalanced form only two variable reactors are required and their reactances are equal at each setting. The circuit is of the bridged-T type. It is derivedfrom a constant-resistance, all-pass, lattice network' in which one branch comprises a generalreactive impedance and the other branch comprises an equal impedance connected to the remote end of a subsidiary network which has a phase shift of 90 degrees or an odd multiple thereof at the operating: frequency f and thus effects an inversion of the impedance. The subsidiary network may, for example, be a T or 1r of reactances forminga low-pass or a' high-pass filter... In

order to provide a'wide range of phase'shift, in

one embodiment the general impedance includes both a capacitor and an inductor, connectedv either in series or in parallel, oneof which is variable. lattice-to bridged-T, one or more additional reactors may be added arbitrarily to the generalv impedance. By a special procedure the lattice may be transformed into an equivalent bridged-T net- Such' a. device'maybe built in the form of a constant resistance structure but, in, order to keep the- To facilitate the transformation from work in which exactly equal variable reactances The nature of the invention: will be more. fully" understood. from the. following detailed. descrip. tion and-byreferencetto the-accompanying'drawing zin whichlike-reference characters areused: to designate similar; or corresponding parts and 1. of which:

Fig. 1. isa-schematic. circuit of the prototypeconstan'taresistance lattice network inrwhich. the seriesbranch .is a general impedance 1 ZA and-the diagonal branch-ze comprisesi a. second impede ance .ZA associated. with. a subsidiary impedance: invertingnetwork N;

Figs. 2 and 3 show the branch ZBtwhenvthe; network! N is a. qr-type :low-passor: highepass filter, respectively;

Fig.3 is; a schematic circuit of'a bridged-Ti network equivalent, except for an 'intrchan'gel of 5 branches,- to the prototype lattice of l ig. 1 .When" the subsidiary network N is aw-type raw-pass: filterqas shownin Fig. 2 and the general impedance ZA is the series type show'n in-Fig. 4;

Fig, 9; is a. network similar to"the "one"shown' in-Fig. 8 except that the high-pass filter of Fig. 3-

is substituted for the low-pass filter v Fig. 10 is a bridged-T network equivalentto' the latticesof Fig.- 1 when N is a, T-type low-pass filter; as shown inFig. 5.and ZA is "theparallel ao F e- 7;

Fig. 11 is a network similar to the one shown" in Fig. 10 except that the high-pass filter of Fig. 6 is substituted for the low-pass fil'ter;

Fig. 12 is a circuit equivalent to the one shown in Fig. 8 after a portion? of "thebri ging branch has undergone an impedance transformation to provide, equal variable impedance Z/2.-- in the bridging and 'shunt 'branchs';

l3 is,a preferredembodiment. of th'e in vention, equivalent at the operatingfr'equencyfc' to.-the-circuit of Fig. 12, in which one of the capacitors-Gin the bridging branch hasbeen eliminated; p 7

Figs. 14, -15,and were other preferred em bodiments derived, respectively, fromthe circuits shown in Figs. 9, 10, and 11;

Figs. 17,18, 19, and :20 are specifiocircuits corresponding, respectively. to, those shown in- 'FigS." 13, 14, :15; and 16 when; the variable impedance Z is constituted by the series combination of the elements L1, C1, and R1 in parallel with a compensating resistor R2, as shown in Fig. 21: and

Fig. 22 is a, curve showing how the insertion phase shift of the network is related to the value of the variable reactance.

Taking up the figures in more detail, Fig. 1 shows schematically the prototype lattice network comprising two equal generalized series impedance branches ZA and a pair of equal diagonal impedances ZB connected between a pair of input terminals l, 2 and a pair of output terminals 3, 4. Only one series branch ZA and one diagonal impedance ZB are shown explicitly, the other corresponding branches being indicated by the broken lines connecting the appropriate terminals. A suitable source of alternating electromotive force may be connected to the input terminals and a load or utilization circuit connected to'the output terminals.

The impedance ZB is made up of a reactive four-terminal subsidiary network N connected to the diagonal branch at the terminals 5, 6 and terminated at its output terminals 1, 8 in an impedance Z. of the same value as the impedance forming the series branch of the lattice. The function of the subsidiary network N is to invert the impedance ZA with respect to R0, the image impedance of the lattice, and therefore N also has an image impedance equal to R and an image phase constant which is equal to an odd multiple of 90 degrees.

If the impedance ZA is essentially a pure reactance of value XA the lattice network will operate as a phase shifter having an image impedance R0 and an insertion phase shift given by It is seen, therefore, that the phase shift introduced depends upon the reactance of the impedances ZA and may be varied by adjusting the value of XA. As will be explained below, the effects of parasitic dissipation in the reactive elements forming ZA can be compensated for to a large extent, so that the insertion loss of the lattice is substantially constant and independent of the value of X1!- Fig. 2 shows the configuration of the branch ZB when the network N is a 1r-type low-pass filter comprising a series inductance L with a shunt capacitance C connected at each end thereof. In order for the network N to have an insertion phase shift of 90 degrees at the operating frequency fo the elements have the following values:

Fig. 3 shows the branch Z13 when N is a qr-type high-pass filter made up of a series capacitance C and two shunt inductances L, the values of which are given by Equations 2 and 3.

Fig. 4 shows a specific form of the impedance ZA suitable for use with the 1r-type networks of Figs. 2 and 3 to permit the conversion of the prototype lattice of Fig. 1 to a physically realizable equivalent bridged-T network, as explained below. It comprises the series combination of an inductance L, a capacitance C and an impedance Z yet to be determined. The elements C and L have the values given by Equations 2 and 8.

4 At the operating frequency In, L and C are resonant so that the impedance of ZA is equal to Z.

Fig. 5 shows the branch ZB when N is a T-type low-pass filter made up of two series inductances L and an interposed shunt capacitance C, and Fig. 6 when N is a T-type high-pass filter constituted by two series capacitances C and an interposed shunt inductance L. Here, again, the values of C and L are found from Equations 2 and 3.

Fig. '7 shows a specific form for the impedance ZA suitable for use with the T-type networks of Figs. 5 and 6 to permit the realization of a physical bridged-T network equivalent to the lattice of Fig. 1. It comprises the parallel combination of a capacitance C, an inductance L and an impedance Z. The elements 0 and L have the values given by Equations 2 and 3.

Fig. 8 shows a bridged-T network equivalent to a lattice in which each series branch has the configuration shown in Fig. 2, each diagonal branch is an impedance ZA, and ZA is of the form shown in Fig. 4. This lattice, it will be recognized, is the same as the one shown in Fig. 1 except that the branches ZA and the branches Zn are interchanged. The bridged-T network of Fig. 8 comprises two series capacitances C, an interposed shunt branch made up of an inductance L/2 and an impedance Z/2 in series, and a bridging branch composed of an inductance 2L in series with a, capacitance 0/2, the latter being shunted by the series combination of a second inductance 2L, a second capacitance C/2 and an impedance 2Z. The impedance from terminal l to terminal 3 of the bridged-T is exactly twice that of each series branch of the prototype lattice, and the impedance from terminals l and 3 taken together to terminals 2 and 4 is exactly half that of each diagonal branch of the lattice.

Fig. 9 shows another bridged-T network which is equivalent, at the frequency in, to the circuit of Fig. 8. It is derived from a prototype lattice in which the network N is a high-pass vr-type filter, as shown in Fig. 3, and the impedance ZA has the form shown in Fig. 4.

Fig. 10 shows an unbalanced bridged-T network which is the equivalent of the prototype lattice of Fig. 1 when the network N is a T-type low-pass filter, as shown in Fig. 5, and the impedance Z. has the configuration shown in Fig. '7.

The bridged-T network of Fig. 11 is similar to the one shown in Fig. 10 except that it is derived from a prototype lattice in which the network N is a T-type high-pass filter as shown in Fig. 6.

Each of the circuits shown in Figs. 8, 9, l0 and 11 includes an impedance 2Z in the bridging branch and an impedance Z/2 in the shunt branch. In order to adjust the insertion phase of the network, these impedances are made variable, as indicated by the arrows, and for convenience may be coupled together under a single control, as indicated by the broken line connecting the arrows.

The construction and adjustment of the phase shifter can be further simplified by making the variable impedance in the bridging branch equal to the one in the shunt branch. Fig. 12 shows how the circuit of Fig. 8 may be modified to accomplish this by introducing an impedance transformation into the bridging branch. This involves taking the capacitance 0/2 out of the upper parallel arm, doubling its value, and placing it on the outside next to the capacitance 2L. The

ssume inductance 2L in the upper arm now becomes L/2 andtheimpedan'ce-2Z becomes Z/2. 'In the lower arm, the capacitance 0/2 becomes C. In Fig. 12 the two variable impedances Z/2 are now equal at all settings. The circuit of Fig. 12 is the exact equivalent of the one shown in Fig. 8.

Fig. 13 shows a further simplification that can be made in the circuit of Fig, 12 by removing the capacitance 0 next to the inductance 2L and reducing the value of the latter to L. At the operating frequency f0 an inductance L has the same impedance as the series combination of an inductance 2L and a capacitance C. That this is true *is apparent from the following considerations. First, divide the inductance 2L into two equal parts, L and L. Nowone inductance L will-resonate with C at f0 and the combination will have zero reactance. Therefore, C and one of theinductances L may be removed, leaving only the other inductance L, as shownin Fig. 13 which is a preferred embodiment of the invention.

Fig. 14 shows another preferred embodiment obtained from the circuit of Fig. 9 in the same way-that Fig. 13 is obtained from Fig. 8.

Figs. 15 and 16 are two other preferred embodiments of the invention obtainable by appropriate transformations of the networks of Figs. 10 and 11, respectively, in a manner analogous to that described above in connection with Figs. 12 and 13. In the circuits of Figs. and 16 the variable impedances in the bridging and shunt branches are equal but each is equal to 2Z; instead of Z/2 as in the networks of Figs. 13 and 14. The networks of Figs. 15 and 16 are electrically equivalent to the prototype shown in Fig. 1.

All that remains to be determined is the configuration of the general impedance Z. This may include only a single variable reactance, either an inductance or a capacitance. However, Z preferably comprises aninductance L1 and a capacitance C1 connected in series, as shown in Fig. 21. These preferably resonate at f0 and either or both may be variable. The series resistance R1 represents the effective resistance of the elements L1 and C1 at in for an average setting of the adjustable element'or elements. The shunting resistance R2 is included to compensate the effect of the resistance R1 and its value is so chosen, as explained below, that the insertion loss of the phase shifter is substantially independent of the setting of the adjustable element.

Figs. 17, 18, 19 and showcomplete phase shifting networks in accordance with the invention corresponding, respectively, to the circuits of Figs-13,- 14, 15 and 16 when the impedance Z has the configuration shown in Fig. 21. In Fig. 17 the variable element in the bridging branch and the variable element in the shunt branch, under unitary control, are the capacitances 201. In Fig. 18 these elements are 'the inductances I i/2, in Fig. 19 they are the capacitancesCfi/Z, and in Fig. 20 they are the inductances 2L1.

The performance ofthe phase shifters shown in Figs. 17, 18, 19 and 20, at the operating frequency f0, is best described in terms of the prototype lattice of Fig. 1. As already stated, Figs. 19 and 20 are the equivalent of Fig. 1, and Figs. 17 and Bare equivalent to Fig. 1 if the series and diagonal branches of the lattice are interchanged.

In Fig. 1 it will be assumed that the network N has a phase shift of 90 degrees, or an odd multiple thereof, at it, thatthe impedance ZA has the configuration-shown in Fig. 4 or Fig. 7, and that the impedance Z has the form shown in Fig. 21. Si'nceL and C are resonant inFig. 4 andfantiresonant in Fig. '7, the impedance 'ZA will ice-equal to the impedance Zat To. Therefore, in Fig. 1, the insertionlos's a-in nepers and theins'ertion phase shift 5 in radians are'give'n by the expression which may also be written in terms of the admittance Y as M4219: e R,Y-1 (5) where In the case under consideration 1 1 E; R.+J'X1 (7) and r l l :27rf L1m so we have the relation 0 R0 at +Rr+iX1+ 1 5 (9) n R0 1 2 R1+j 1 Now, if we set Equation 9 may be Written as R ny a R,, R0 RIR2 +1fi (ll) 2; OF R. R, R R

from which and X 'Ro 1 B 2 tan RIB/2 (13) It is seen from Equation 12 that the insertion loss is independent of the valve of X1 when R1 and R2 satisfy the relationship 10). Therefore, if the eifective resistance R1 associated with the elements C1 and L1 does not change with X1 and if the compensating resistance R2 is determined by'Equation 10 the loss does not change as the phase shift ,8 is varied. In practice it is found that R1 does not change appreciably as X1 is varied, especially if X1 is varied by-adjusting the capacitance C1, as inFigs. 1'7 and 19. 'To minimize'the change in R1 these capacitances are preferably furnished by capacitors having air as the dielectric.

From Equations 13 and 10 the following expressicn may be derived:

6 2 tan"% .(14) where o MR I 0 'i'fJl (15) It is clear, therefore, that the-phase shift 13 can be determined when the reactance X1, the resistance R1 and the image impedance R are known. The curve of Fig. 22 shows the phase shift 13 in degrees plotted against the ratio Xl/Ro. If the reference phase is taken as zero when this ratio is zero, it is seen that the phase increases to +180 degrees as the ratio increases to plus infinity and decreases to 180 degrees as the ratio goes to minus infinity. If a greater phase shift is required, two or more of the phase shifters may be operated in tandem. The total phase shift of the combination will be the sum of the phase shifts of the individual networks, since the networks have a constant resistance image impedance at each end.

As an illustrative example appropriate values for the elements of the phase shifter shown in Fig. 18 will now be worked out. It will be assumed that the image impedance R0 is 100 ohms and that a phase shift range of :90 degrees is required. If dissipation in the elements is neglected, it is necessary that the reactance X1 be adjustable from 100 ohms to +100 ohms. For example, the adjustable inductance L1 as shown in Fig. 21 may have a range of 900 ohms to -1100 ohms at the operating frequency f0 and the capacitance C1 in series therewith will then have a fixed reactance value of 1000 ohms at that frequency. The combination will thus vary from 100 ohms to +100 ohms as the inductance L1 is adjusted. Now if the effective resistance R1 is ohms, R'o is found from Equation to be equal to 101 ohms. From Equation 10 the proper value of the compensating resistance R2 is found to be 1010 ohms, in order to make the loss of the network independent of the phase setting. The flat loss a is found from Equation 12 to be 1.73 decibels. Now, when dissipation is taken into account, since R'o is 101 ohms the reactance change will have to be increased from $100 ohms to 110]. ohms to provide the full :90- degree phase shift. In this example the elements of Fig. 18, therefore have the followin values:

and fl) is the operating frequency.

The phase shifter may, of course, be built in any of the other equivalent forms shown in Figs. 1'7, 19 and 20 and the elements evaluated by applying the simple factors indicated. The choice of structure may be influenced, among other things, by the behavior of the network at frequencies other than the operating frequency ft. The networks shown in Figs. 18 and 20 will pass frequencies below in and tend to suppress frequencies above f0, while the reverse is true of the networks of Figs. 1'7 and 19.

What is claimed is:

1. A variable phase shifter of the bridged-T type comprising two series reactances each of value X at the operating frequency f0, an interposed shunt branch comprising a reactance of value -X at in in parallel with an arm comprising a third reactance of value X in series with the parallel combination of a reactance of value 2X and an adjustable reactive impedance of value Z, and a bridging branch comprising a second reactance of value 2X in parallel with a second adjustable reactive impedance of value Z, X being approximately equal in magnitude to the image impedance R0 of the phase shifter.

2. A phase shifter in accordance with claim 1 in which X is inductive.

3. A phase shifter in accordance with claim 1 in which X is capacitive.

4. A phase shifter in accordance with claim 1 which includes two resistances each of value 2R2 connected in parallel, respectively, with each of said adjustable reactive impedances, R2 approximately satisfying the relation R R2 R.,

where R1 is the effective resistance of each of said adjustable reactive impedances at said frequency f0.

5. A phase shifter in accordance with claim 1 in which each of said adjustable reactive impedances comprises the series combination of an inductor and a capacitor.

6. A phase shifter in accordance with claim 5 in which said inductor and said capacitor are resonant at approximately the frequency in when the phase shifter is set for the mean phase shift of the range.

'7. A phase shifter in accordance with claim 1 in which each of said adjustable reactive impedances comprises a variable capacitor.

8. A phase shifter in accordance with claim '7 in which said variable capacitors are under unitary control.

9. A phase shifter in accordance with claim 1 in which each of said adjustable reactive impedances comprises a variable inductor.

10. A phase shifter in accordance with claim 9 in which said variable inductors are under unitary control.

11. A phase shifter in accordance with claim 1 in which said adjustable reactive impedances are substantially duplicates of each other. 7

12. A variable phase shifter of the bridged-T type comprising two series capacitors each of value C, an interposed shunt branch comprising an inductor of value L in parallel with an arm comprising a third capacitor of value C in series with the parallel combination of an inductor of value 2L and an adjustable reactive impedance of value Z, and a bridging branch comprising a second inductor of value 2L in parallel with a second adjustable reactive impedance of value Z, C and L each having at the operating frequency f0 a reactance which is approximately equal in magnitude to the image impedance R0 of the phase shifter.

13. A phase shifter in accordance with claim 12 in which said adjustable reactive impedances are substantially duplicates of each other.

14-. A phase shifter in accordance with claim 12 which includes two resistances each of value 2R2 connected in parallel, respectively, with each of said adjustable reactive impedances, R2 approximately satisfying the relation where R1 is the efiective resistance of each of said adjustable reactive impedances at said frequency f0.

15. A phase shifter in accordance with claim 12 in which each of said adjustable reactive impedances comprises the series combination of an inductor and a capacitor.

16. A phase shifter in accordance with claim 15 in which said last-mentioned inductor and capacitor are resonant at approximately the frequency f0 when the phase shifter is set for the mean phase shift of the range.

17. A phase shifter in accordance with claim 12 in which said adjustable reactive impedances are under unitary control.

18. A variable phase shifter of the bridged-T type comprising two series inductors each of value L, an interposed shunt branch comprising a capacitor of value C in parallel with an arm comprising a third inductor of value L in series with the parallel combination of a capacitor of value 0/2 and an adjustable reactive impedance of value Z, and a bridging branch comprising a second capacitor of value C/2 in parallel with a second adjustable reactive impedance of value Z, C and L each having at the operating frequency in a reactance which is approximately equal in magnitude to the image impedance R0 of the phase shifter.

19. A phase shifter in accordance with claim 18 in which said adjustable reactive impedances are substantially duplicates of each other.

20. A phase shifter in accordance with claim 18 which includes two resistances each of value 2R2 connected in parallel, respectively, with each of said adjustable reactive impedances, R2 approximately satisfying the relation R1 RF where R1 is the efiective resistance of each of said adjustable reactive impedances at said frequency f0.

21. A phase shifter in accordance with claim 18 in which each of said adjustable reactive impedances comprises the series combination of an inductor and capacitor.

22. A phase shifter in accordance with claim 21 in which said last-mentioned inductor and capacitor are resonant at approximately the frequency f0 when the phase shifter is set for the mean phase shift of the range.

23. A phase shifter in accordance with claim 18 in which said adjustable reactive impedances are under unitary control.

PAUL H. RICHARDSON.

No references cited. 

